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dc.contributor.authorPagnini, G. 
dc.date.accessioned2016-06-13T13:33:23Z
dc.date.available2016-06-13T13:33:23Z
dc.date.issued2014-12-31
dc.identifier.issn0378-4371
dc.identifier.urihttp://hdl.handle.net/20.500.11824/193
dc.description.abstractIn the present Short Note an idea is proposed to explain the emergence and the observation of processes in complex media that are driven by fractional non-Markovian master equations. Particle trajectories are assumed to be solely Markovian and described by the Continuous Time Random Walk model. But, as a consequence of the complexity of the medium, each trajectory is supposed to scale in time according to a particular random timescale. The link from this framework to microscopic dynamics is discussed and the distribution of timescales is computed. In particular, when a stationary distribution is considered, the timescale distribution is uniquely determined as a function related to the fundamental solution of the space-time fractional diffusion equation. In contrast, when the non-stationary case is considered, the timescale distribution is no longer unique. Two distributions are here computed: one related to the M-Wright/Mainardi function, which is Green's function of the time-fractional diffusion equation, and another related to the Mittag-Leffler function, which is the solution of the fractional-relaxation equation.
dc.formatapplication/pdf
dc.language.isoengen_US
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.subjectFunctions
dc.subjectContinuous time random walks
dc.subjectContinuous-time random walk models
dc.subjectFractional diffusion equation
dc.subjectMittag-Leffler functions
dc.subjectNon-Markovian master equation
dc.subjectStationary distribution
dc.subjectSuperposition
dc.subjectTime-fractional diffusion
dc.subjectPartial differential equations
dc.titleShort note on the emergence of fractional kineticsen_US
dc.typeinfo:eu-repo/semantics/articleen_US
dc.identifier.doi10.1016/j.physa.2014.03.079
dc.relation.publisherversionhttp://www.sciencedirect.com/science/article/pii/S0378437114002908
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessen_US
dc.type.hasVersioninfo:eu-repo/semantics/acceptedVersionen_US
dc.journal.titlePhysica A: Statistical Mechanics and its Applicationsen_US


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